Note: this document is optionally non-linear, the position
of text and boxes relative to other text and boxes is
not definitive.Thus it may be read either linearly or
by dodging about, which ever manner best suits your style.
Some may find the text outside the boxes difficult to
follow at first. In which case, it may help to examine
the boxes first.

Because the topics being discussed often interact, for
clarity of reasoning some information is repeated in different
sections. Thus the section headings are not intended as
‘separate’ categories, but as a help to organisational
referencing. For further comment see below.

Introduction

By Aristotelian logic, I mean category logic, excluded-middle
logic, on/off logic, either/or
logic.
No greys – only black and white. This false ‘logic’
lies at the heart of authoritarianism, conflict, and a
great deal of inadequate ‘science’.

You are either for us or against us.He ‘is’ ‘good’ or he ‘is’ ‘bad’
.You did, you didn’t.‘Dyslexia’
is caused by ‘genetics’ or ‘brain trauma’.

Aristotelian logic is also called by some, ‘Descartian
logic’.

The problems caused by Aristotelian logic are legion
and accumulate. They include the mis-use of ‘properties’,
as well as a failure to match ‘theory’ to
the real world. Those who take a pragmatic/empirical approach
are less likely to be caught by the consequences of this
theoretical paradigm. There is much more on the ‘property’
problem in the MetalogicA series of documents – the
Confusions of Gödel.

In this document, the elements in the green and yellow
boxes refer to the fundamentals of rational communication.
Much of the rest of the document is given over to describing
the fundamental errors in Aristotelian logic.

reality

You have been raised in an unsane culture. Driving that unsanity is a slavery to words.
For sanity, you must learn to attend to reality outside
yourself. The woods and the trees are real. To discuss
them adequately, you must learn to communicate with clarity.
That means understanding the confusions of language that
are rife in western culture.

Every time you use a word you make a choice, you form
a category to which only you have access.

The errors of Aristotelian logic are so pervasive that
they cannot be sorted by one or two simple fixes. Thus
I must tackle them in parallel until you may grasp the
problems as a gestalt, or else take
a leap of faith in completely revising your expressive
mental set. Until that point, you are liable to attempt
to drive a broken cart that will not go.

It is not enough to attempt to fix Aristotelian logic
if you are to cogently discuss issues such as mathematics,
politics, philosophy, psychology, economics and the like
in a sane and rational manner. For the invasive elements
of Aristotelian logic make rational discussion of subtle
real-world issues effectively impossible.

It is not what you think that causes the majority of problems in communication,
it is the way in which you think
and the manner in which you communicate.

The major part of this document lists the fundamental
problems with Aristotelian logic. It is produced for those
who need to understand why they should consider revising
a system that has contributed to such considerable gains
for humans over the last two and a half millennia. This
document is also for those who need to understand where
the problems lie in the standard cultural paradigm. By
understanding this, people may be persuaded to release
their grip on an old familiar comfort blanket, preparatory
to reorganising their thinking and to considering a more
rational model. Further, this document is for those who
wish to understand the teaching process.

There are other errors, which are intrinsic to the use or misuse of Aristotelian logic, that have
been studied down the centuries. I have listed a couple
of sites that provide summaries of these internal problems
on my links page. This document is concerned with the fundamental, extrinsic errors of Aristotelian categorical
logic, these underlying Aristotelian assumptions may be
regarded as empirical falsehoods.

These Aristotelian falsehoods are empiric errors. Aristotelian logic simply does not conform to,
or express, the nature of the world as it is. Aristotelian
logic engenders a simplistic but erroneous model of reality.

To add to difficulties, as long as the Aristotelian errors,
listed and linked in this document, are so pervasive and
habitual in the language of our culture, I am to a degree,
constrained to use common words, which words may easily
be misread. Therefore, as I move from section to section
here in this document and highlight the various fundamental
errors of the Aristotelian language structures, keep in
mind that a degree of ‘relaxation of rigour’ is necessarily inherent if I am to be spared endless qualification
of each detailed use of each term.

For example, when I refer to ‘a’ word, keep
in mind that each usage is new (see also following section)
and further that neither ‘the’ word, nor its referent, is entirely separate in reality.
It is merely convenient to treat it thus at a particular
‘point’ in the text. The wide use of quotation
marks is used to keep you alert to these problems.

Aristotle had trouble deciding
whether ‘the sitting man’ was a different object from ‘the standing man’. The reality
is that there are no separate objects, just our choices
at individual times to treat the world in terms of separate
‘objects’. Thus we may treat the sitting man
as a new object, or as a continuum with the standing ‘object’,
entirely at our whim. Separations are made by our personal
decisions for our particular purposes, at ‘all’
‘times’.

Because of the interactive quality
of the difficulties presented by Aristotelian (on/off
or digital) semantics, I have repeated many of the ideas
to some degree in various of the sections of this document.

It is more than possible that various readers may find
some phrases ambiguous. Such problems differ from individual
to individual; it is therefore not possible for me to
remove ‘all’ these difficulties without feedback
from readers. If you do find difficulties understanding
parts of this document, it would help if you e-mail me with your difficulty. I will attempt to answer your
queries and to improve the text where, to me, that appears
to be useful.

We may iterate to obtain
as much accuracy as we require, or have the energy or
patience to pursue, but we may never obtain completion
or certainty. In reality, such absolutist objectives are
illusory for humans. See also the
logic of ethics

Each individual has their own notions and
intentions. As with any object or objective, the purpose of communication becomes one
of negotiating with others to achieve mutually satisfactory
outcomes.

Effective communication is done by a sequential
process of continually refining understanding between
individuals. This process includes the settling upon definitions
of any approximate objects to be discussed, the objectives
to be discussed, and the words with which those objects
are to be discussed.

Some may wish to
be very careful and precise in their attempts to understand
others well. Those who do not wish to put in such effort
tend to be called ‘lazy’, while those called
‘lazy’ tend to call the careful, ‘neurotic’!
Thus is the intolerance of differences.

If in doubt check, always seek feedback.
Is it that plate or this? Do you mean here or here? What
do you mean by that word? Show me how you use that word
using real objects that I can see, as a means to demonstrate.

Always, always, seek
feedback

For effective relationships, negotiation
is central. Negotiation is a form of iteration. Often
such negotiation becomes a matter of power; I discuss
this further infeedback
and crowding and in the
logic of ethics.

categories

One day, Manjushri stood outside the gate when Buddha
called to him. "Manjushri, Manjushri, why do you
not enter?"

"I do not see a thing outside the gate. Why should
I enter?" Manjushri replied.

The above is a Buddhist koan. [5a] Such ‘stories’ are designed to evoke satori (enlightenment), that is, the realisation that all
words are grass.

All categories are arbitrary;
categories do not exist ‘out there’. Once
your mind is ruled by category, you are in a mind-trap;
you are unable to think with clarity or independence.
To think clearly, your mind must be still and clear of
any words.

I don’t wish to be gobbled . For
example, frogs dive from predators, and plants produce
poison and thorns to discourage others from turning them
into dinner.

Categorisation is necessary for life and survival; categorisation
is a matter of pragmatism.

The first twelve chapters of Book 7 of Aristotle’s Politics sketch the connection between philosophy
and politics: namely, that the highest purpose of a city-state
is to secure the conditions in which those who are capable
of it can live the philosophical life. Such a life, however,
lies only within the capacity of the Greeks, whose superiority
qualifies them to employ the non-Greek tribal peoples
as serfs or slaves for the performance of all menial labour.
Thus, citizenship and service in the armed forces are
considered to be the exclusive rights and duties of the
Greeks.

At about the same time, Aristotle composed the work,
now lost, On Kingship, in which he clearly
distinguishes the function of the philosopher from that
of the king. He alters Plato’s dictum – for
the better, it is said – by teaching that it is
not merely unnecessary for a king to be a philosopher,
but even a disadvantage. Rather, a king should take the
advice of true philosophers; then he would fill his reign
with good deeds, not with good words.

Aristotle formalised the categorical thinking that has
evolved into a dogma in western society. As a dogma, it
has been extremely useful in analysing the world (Aristotle
called his logical system ‘analytics’). However,
it has also tended to inhibit creative and realistic thinking.

The arrogant and rather dull Bernard of Clairvaux said
of Abelard, “you will find something more in the
woods than in books. Woods and stones will teach you what
you cannot hear from masters.” [7]

Abelard kept discussion of ‘god’ out of his work on
logic. In a passage in his commentary on Porphyry, the
question of ‘god’s’ intellect arises
in the context of the problem of knowledge of the future.
‘god’s’ perception of the future, Abelard
says, is most sensibly resolved by saying that:

His substance, which alone is unchanging and simple,
is varied by no conceptions of things nor by any other
forms. For; although the custom of human speech presumes
to speak of the creator in the same way as of creatures,
by calling Him provident or intelligent for example,
nevertheless nothing in Him should be, or can be, understood
as distinct from Him: neither perception nor any other
form. Therefore any question about perception is irrelevant
so far as God is concerned. [8]

Abelard also tries to make his contemporaries understand
that there is a fundamental difference between talking
about ‘god’ and, alternatively, discussing
what others have said of ‘god’. It is but
a short step to substitute in the writings of the brighter
of the scholastics, the term ‘god’ with the
word ‘reality’, whence texts that may read as obscurantism and mysticism to a modern starts
to make eminent sense.

Thus Abelard, in the 12th century, is concerned with
the connectivity of ‘objects’. More recently,
Brouwer [9] and others have expressed
similar concerns through an attack on the Aristotelian
dogma of the excluded middle. By better understanding
the varying semantics of considerable thinkers down the
ages, it is clear that, despite their different words,
their meanings are often rather similar. Again, this is
a major concern in Abelard’s monumental Sic
et Non.
For more details on the problem of the excluded middle,
see the
logic of ethics.

words

Words are, by their usage and near natural (physical)
reality, categories chosen by individuals. The words are
not ‘identical’ with the ‘substance’
(real matter) at which individuals point, when they use
those words. Reality does not somehow magically split
when we choose our usage of categories; category merely
helps us to communicate and to mediate our relationships with reality.

We likewise treat the words as separate items and imagine
that, in turn, those words are capable of referencing
separate items. For further discussion in a more complex
context, see Feedback and crowding.

Thus to control our world and to communicate about it,
as a pragmatic act we section off
reality, in order to enable us to handle complex matters
within our very limited understanding. We build up our
understanding, first by accumulating rather minor ‘bits’
of information about the world, and then by attempting
to synthesise patterns from the cacophony of reality;
see also MetalogicB1
– Decision Processes.

So we act as if reality is sectioned into ‘parts’. Reality
however, remains universally interconnected. The moment we lose sight of this fact, we move toward hubris and error. As human animals, we
further tend to make a strong separation between our ‘individuality’
and the ‘rest of the world’. But again we
are connected, we are ‘part’ of the universal reality. Words are ‘part’
of reality. The words that we treat as ‘separate’
are also involved as noises or marks on paper or cathode
ray tubes in the universal reality.

The human enters the world without language. Because
language is so very useful to human progress, a central
objective of education is to develop language usage; but
the process goes too far. Language is near universally
taught in such a manner that it ceases to be merely a
tool for communication, but become a straitjacket upon
the thinking progress. This extends until most humans
cannot think outside ‘the’ mass of words circulating
in their consciousness that becomes a substitute for independent, reality-based analysis.
That is, humans become addicted to language, they become
the servants of local language structures instead of the
masters of language. [12]

We are not required to throw all previous knowledge of
logic to the winds as useless. But we must considerably
increase the rigour of reasoning and, from the earliest age, train different habits of thinking
about language if we are to free ourselves from the language
trap.

To establish sane habits of language usage, it is necessary
to develop usage that is both in accord with the human
condition and in accord with the nature
of the reality in which we find ourselves enmeshed.

The categories we use for habitual thinking are fundamentally
false to reality, as to some degree they are bound to
be. They still must conform to reality to such an extent
that they are reasonably useful, easily understood and
widely acceptable.

Thus for useful language structure, it is essential that
I proceed with an assumption that my reader will agree
to the categories I establish. The categories are based
upon what I have found to work; that is, the categories
are pragmatic. They are most definitely
not static; they are intended to be demonstrable to reasonable
people upon the sole criterion of pragmatism. These categories
are assertions about how communication will work in practice. I am widely convinced that the present
underlying, unexamined premises abroad in western society
do not work in the real world much
of the time, particularly when discussion gets
complicated. I am convinced that the principles I am stating
will and do work, however complex discussion becomes.
That is, I am establishing empirically founded assertions that are structurally capable of negation.

If we become caught in the separated construction that
we assemble for our own feeble-minded convenience, if
we start to ‘think’ in words rather than control
the words for our communicative purposes, we move beyond
sanity.

Brouwer in 1907 put it thus:

However, in general the consideration of sequences
and consequent going back from the end to the means,
where intervention appears easier, show themselves
very efficient tactics from which mankind derives
its power. Man succeeds in discovering regularities
in a limited field of phenomena independent of other
phenomena, which consequently can remain completely
latent in the intellectual consideration of the former. [13]

The development of ‘religion’ is the history
of development of world-views among steadily more sophisticated
societies. Gradually the world-views have moved from dogma
to empiricism, as we gained better understanding. We often
hear this called the advance of ‘science’.
But ‘science’ is also a form of religion.

Aristotle, in Posterior Analytics, imagined
that science could be placed upon fundamental axioms.
As understanding has progressed, it has become clear that
effective progress is based in empirics. That is, all
ideas of our strange home are subject to constant revision
as new data is gathered. Step by step, traditional ‘religion’
has been driven out of large areas of human understanding,
as empirics advances over dogmatic axiomatics.

Aristotle, in Politics, also imagined humans
to be essentially political animals and discussed political
systems in terms of the various characters of citizens.
That is, he grounded politics in views concerning human
psychology. Ever since, the field of human behaviour has
been claimed by various axiomatic approaches of differing
societies.

Dogmatism has yet to be driven
from human concepts of individual and social behaviour.
It is my intention to lay the logical basis for achieving
that end.

Naturally the extent of knowledge concerning the human
state has steadily grown down the centuries, as it has
in all studies of interest to humans. But systematic progress
only develops when descriptions that ‘reasonably’
reflect reality are established. Aristotle called the
human a rational animal, by which he intended the meaning:
an animal that uses language.

Psychological study is so complex that the Aristotelian
axiomatic system of itself introduces
fundamental errors of ‘thought’.

The wish for any Aristotelian-based ‘theory of
everything’ imbibes ‘the’ error.

To understand communication, it is essential
to understand that each person uses each word differently,
both from each other and also on each occasion
of usage.

We use the words primarily to point at
‘objects’ in the real world. Words are similar
to sticks with which we might choose to point.

The use of the verb ‘to be’
has a high propensity to confuse the word with the object
at which we might point. ‘That is a house’
we might say, when what we mean is, ‘I wish you
to direct your attention to that house over there.’
The thing to which we point is not a ‘house’.
It is an arrangement of real matter in which some may
well choose to live. And once again that sneaky word ‘is’
creeps in to our conversation. What is ‘really’
meant is that I call that object over there a ‘house’
and wish to discuss that object with you.

The introduction of the word ‘is’
has a considerable ability to confuse the mind of the
humans who spend so much of their focus of attention upon
words. For sanity, the focus must be on the real material
of nature, not upon the words that describe. One must
always attend to observing the ‘objects’ to
which the words point.

Unlike Manjushri, the human child is conditioned
to think in words as if those words are the reasonable
objects of thought. Humans learn to ‘think’
in words, rather than merely acting impulsively in the
world. While this brings great benefits, it also brings
great confusions and dangers, particularly when situations
become complex.

The real world does not sit quietly with
our pre-arranged words. The world is in constant flux
and change. If we learn to think in
words, that process has the undesirable side effect of
inclining us to think with in the limited and confused
categories we have imbibed through language. Thus language
limits our flexibility of thought.

Manjushri has become aware of this, as
some humans do. Manjushri is ‘enlightened’.

1.

Most who come to the
state of satori have proceeded from the
inchoate ‘natural’ state of the newborn
who has no language, that is they may be said to
be ‘pre-verbal’.

2.

Then they move onward
to the ‘verbal’ state of using language
upon which they become addicted, and by which they
become trapped.

3.

Some few move thence
to satori or enlightenment or to a ‘post-verbal’
state, when they become aware that real independent
thought must live in a world of silence beyond words.

Most never move to stage three. Far better
that children were taught in such a manner that they never
become addicted to stage two.

This may be achieved by constantly making
the child aware of the differences between language and
the ‘outside’ world. “I call that object
a plate”, “that is a picture of a duck”
in place of “that is a duck” or “that
is a plate”.

It is not required that one becomes neurotic,
just that you establish clearly in the child’s mind
the awareness of the nature of language as useful for
communication, but deadly and deadening for enlightened
thought.

Playing games with words is also useful.
Calling the plate a duck and the duck a plate reinforces
the separation and flexibility of mind.

As the child develops language, prior to
becoming too fluent, it is common for the child who has
learnt the word for daisy to decide that all flowers are
daisies, or to call a sheep a little white camel. Children
are far more flexible until the addictive forms of language
intervene and destroy their flexibility. Our language
teaching thus tends to teach the young to think in rigid
manner, which then limits their potential. That is, teaching
tends to teach how not to think efficiently, the very
reverse of any sane objective.

True
thinking is silent

Words going around and ‘around in
the head’ are destructive of sanity. If this happens
to you, you need to learn to refuse words every time they
enter your head/‘thinking’. To achieve this,
it is an assist to concentrate on looking at and feeling
some real-world object of your choice, such as a stone
or your favourite teddy bear.

Words are for communicating; they will
be there when you need them.

counting
is not simple

A great unexamined assumption down the ages has been
that counting is some simple process which all can understand;
counting is no such ‘thing’. We are taught
a series of ordered magical grunts in childhood, ‘one’,
‘two’, ‘three’, etc. We learn
to associate these magic noises with what we imagine to
be ‘objects’.

No ‘two’ humans ever occupy the ‘same’
space-time. The space-time position currently occupied
by one human can never be occupied by another human. Everything
each of us sees is necessarily ‘different’
from that seen by others, for we are not the other. We
are our ‘separated’ selves. At the core of
our language usage is an assumed separateness of individuals
and the pragmatic separation of words. That separation
includes the words called ‘numbers’ (also
see box III).

numbers
or objects

The meaning of the word ‘one’
is synonymous with the meaning of
‘thing’ or ‘that’ or ‘the’
or ‘bit’ or ‘object’

Numbers have no magical essence. Numbers are no different
in nature or type than any other words. ‘Two’
just means “object and another object”. Numbers
are words, they are not more than words and they are not
less than words. There is no essential difference between
language and mathematics. To attempt to teach mathematics
as somehow separated from language is poor and confused
pedagogy.

Humans use numbers to point at
objects, just as they use other words to point at objects.
Words point at objects, just as a stick may be used to
point at objects. The words themselves are as much real-world
objects as are the objects at which we point. A word is
marks on paper, speech causing a mass of air to vibrate,
an electro-chemical configuration in our real brains,
and so on.

An ‘object’ is just what any individual human
decides at that moment is an ‘object’. Objects
do not somehow ‘exist in their own right in the
world’. As Manjushri is
aware, all is one. It just happens to be convenient and
useful for humans to separate out and focus upon ‘bits’
of that unified reality.

When a human decides to refer to some ‘section’
of reality, in order to examine ‘it’ or to
communicate about ‘it’ with another human
(object), it is not possible for either human ever to
understand ‘exactly’ what the other human
is focusing upon. It is not even possible for humans to
‘fully’ delineate or define anything. The
best that may be hoped for is approximations (see section
on ‘complete’).

Even the human doing the pointing
is limited, to the extent that they cannot focus upon
the microscopic detail, nor keep up with the ever-changing
movement of the atoms and shifts in space.

Remember, the human doing the pointing is subject to
constant change as well. Thus on repeating a word, the
human will have changed and the supposed
object to which the human points will also have changed.

Every use of every word by
every person is different

One might say every object is different
at all times, but naturally we cannot pin down any object
to make such a statement fully meaningful. Nor can we
fully establish a separateness of objects, including a
separateness of ourselves.

All ‘objects’ are
in flux

Fortunately these difficulties, and differences or changes,
are not so great that we cannot use words with pragmatic
effect. Despite the problems, we can communicate sufficiently
effectively to enable and enhance our everyday life and
survival, but we are wise to keep in mind the very real
limitations of language.

We may proceed by not worrying too much about the inevitable
inaccuracy of all language usage, thus accepting
a generalised relaxation of rigour. That is, by accepting
sufficient similarity as a replacement
for any ambition to some unattainable ‘total accuracy’
or ‘equality’.

II –relativity

The idea of a ‘naughty’ or
‘good’ person or other object, is mis-thinking.
What is really meant is that the other person is acting
in a way that conflicts with, or alternatively, serves
my interests, my ego or my sense of aesthetics. All ‘naughtiness’
or ‘goodness’ is relative to our own individual
objectives or interests, there is no absolute (see the
logic of ethics) standard written in the stars.
We make our own cultural rules according to our power,
our comfort and our tastes.

The description of the relationships of
objects does not require the use of the concept of space.
It requires only measurement of distances between objects.
Time is not some phantasm.

Time is movement

The movement of objects, such as the pendulum
of a clock, we use to measure what we call time.[14a]Thus does time become a matter of the relativising the
movement of one chosen object with another, without a
need to refer directly to the qualities of space.

So modern physics attends to Occam and
ignores space, and merely measures relative movement and
distances. Space does not thereby cease to exist, but
attention is not focused on this most difficult aspect
of reality.

The movement of a ball thrown across a
room may be measured in the framework of the room and
tracked by the imagined regularity of a clock. The room,
also, may be measured in its movements relative to the
earth, as the earth spins and walks around the sun. The
individual, likewise, can be measured and tracked as they
walk upon the earth. Meanwhile, the heart ticks as a clock
within the moving body, as part of the body’s constant internal change or movement.

All change is measured thus. As you speak,
your words take a finite time to reach the ears of another.
Meanwhile your body is in external and internal motion;
so with the body of your communicant; so with the objects
you have chosen for your discourse.

Thus there is no ‘absolute’
‘static’ framework, just sufficient stability
for much everyday discussion. Such limited stability is
not reliable and within complex conversation the instability
can confuse. For sanity it is well to keep this in mind.

Consider four blocks.
Consider an experimenter and a subject. Consider the blocks
going around step by step in a ‘circular’
clockwise motion. Consider the subject exiting from sight
of this ‘clock’. After an interval the subject
returns to find the blocks which appear, to the subject, to be in the original position. If the
subject depends upon this ‘clock’ for their
sense of ‘time’ and if the subject is unable
to distinguish any difference in the position of the components
of the block clock, to all intents and purposes, ‘time’
is static for that subject relative to that clock. Of
course they still have their own heart-beat and a remembrance
of moving out and into the presence of the clock. Without
such remembrance, in the absence of an external clock,
time effectively ceases for that person.

Remember, separations of space and time
are likewise arbitrary.

the
error called ‘equality’

To understand words, it
is necessary to understand that words
have no fixed or certain meaning

Heraclitus said,
“You cannot step into the same river twice”.

You live on a surfboard, the world is constantly
shifting around you and within you. To be effective, you
must learn to ride the surf and to keep your balance,
not attempt to stop the river, or even fuss to speed it
up.

Most attempts to understand words thereby
miss all useful understanding or meaning.

Poincare stated “Mathematics is the
art of giving the same name to different things”. [15]

Skolem writes “The use of the equal
sign in what follows is always to be understood in the
sense that two names or expressions mean or designate
the same thing”. [16]

Knowledge proceeds by empirics. Empirics
is the true arbiter of useful knowledge. ‘Theories’
are current best available descriptions. Theories are
pragmatic patterns of communication. ‘Theories’
are perhaps the most efficient, common means of communicating
our current knowledge in a particular area available at
this time. Theories do not exist as ‘objects’
or ‘things’ in some mysterious hyperspace.

No ‘two’ usages of a word are
the ‘same’. The very ideas of ‘same’,
or ‘equality’, are false to reality. Human
use of the term ‘same’, when used rationally,
means, ‘sufficiently similar that I do not care
about the differences’ or even, ‘I cannot
discern the differences’. Realise that ‘theories’
are, at all times, subject to the different word understandings
of the participants in those communications.

If I fit the pistons into the cylinder
block of an engine, it matters not which piston goes in
which cylinder. Each cylinder has relatively small variations
and each cylinder is formed from differing masses of metal.
For the purpose of an engine this does not matter. So,
we say loosely, all cylinders are ‘the same’,
but of course they are not.

the
error called ‘zero’ or ‘not’ or
‘negative’

Zero has no existence
or meaning outside of context. It is possible to have
no elephants in a room.It is not possible to have no unicorns in a room,
for there are no unicorns not to be in the room.

There is no object
called the empty set. A set is a collection of objects.
Without objects, there is no set.

In both situations, there is a pre-supposition
of individuals in the real world available to be placed
in the collections. One might imagine a set as a collection
of items in a box, in which case there is a real-world
box in which to place the collection. If the box is emptied
of elements, the real box remains.

If there is to be a mental set, it exists
as a real encoding in the brain, ready and available to
take up a list of real-world items. Either the set/box
exists in the real world or it does not. If the box does
not exist, there is no set, empty or otherwise.

The legal right to silence grows from an
awareness that no legitimate inference may be drawn from
that which does not exist. Therefore, in less educated
societies, such rights do not exist. [20] Likewise, what cannot be counted is best treated with
caution. It is very difficult to count that which cannot
be seen, whether it be gods or unicorns.[21]

The
asymmetry of not. To tell you that I have no
high explosives in my pocket does not give you any information
about ‘items’ that may reside in my pocket.
All it tells you is what I say about one kind of object
not being in my pocket. Likewise, to tell you that I don’t
call the four-wheeled vehicle that is resting outside
my cave a dog, does not give you information about what
I do call it. On the other hand, if I do tell you that
I have a hat upon my head, you have a clear idea of a
real-world fact. In the first case, you are left with
a myriad ‘possibilities’. In the second case,
the possibilities are much constrained. Thus, negative
statements give far less information than positive statements.
Negative statements and positive statements are not symmetrical. Yes and no are not ‘opposites’,
they are ‘different’ (see
here for more detail).

Note that a
form of zero is used as a marker in the number 101
and on many scales such as for the measurement of temperature.
For example, the centigrade scale zero measures the temperature
at which water freezes, that is 273 degrees above ‘absolute
zero’, which is a point at which localised movement
(and thus time) ceases. Such conveniences
are not at issue at this point.

the
error called ‘infinity’

We have a system of counting that allows
continuation from any point. Likewise an engine has the
means of continuation from any position. Eventually the
engine wears out and fails, likewise the counter.

What we may call a table eventually ‘wears
out’ or rots away. At some point, we cease to recognise
it as a table; it becomes compost or smoke. Categories
are not permanent. There is no ‘infinity’
that goes on for ‘ever’. Wherever such fictions
are used, they may be replaced with some suitable, very
large number.

Another form, sometimes referred to as
‘infinite’, is but an open system where no
decision as to a stopping point has yet been chosen or
occurred.

the
error called ‘complete’

Much of superstitious ‘religion’
is built upon ‘concepts’ of ‘perfection’.
There is great fear among humans that analysis will lead
to a removal of wonder in a world where wonder is surely
appropriate. It is difficult for fearful humans to adjust
to the reality that insecurity is inherent in uncertainty
and wonder. We live in a wonderland that is both far beyond
our comprehension and our control. Many seek some unattainable
‘certainty’, or a ‘complete’or
‘absolute’ or ‘precise’ understanding,
such are not available. For peace and equanimity, we needs
must accept our reality and limitations, not seek opiates
or escape. Thus the great ‘theologians’ emphasise
the unknowability of ‘god’.

The notion of some
imaginary ‘perfect’ circle is but a statement
about the limited acuity of human visual equipment. The
lack of precision does not amount to the possibility of
some potential ‘perfection’, or ‘certainty’,
somewhere ‘out there’ on some sky-hook. Once
again, it is a matter of maintaining silence when being
tempted to speak of that which does not exist or, at the
least, not introducing entities without cause.[21a]

Similarly, ‘all’ is only used
with legitimacy in the context of a pre-defined set of
‘objects’.

universals
and individuals

For a person to think with flexibility and realism, it
is essential that they learn to think outside words.

Much human communication is through words. There is no
such thing as the opinion of a country, or of any other
group or organisation. Only individuals have opinions.
All else is confusion or rhetoric. People may act in alliances,
but there is no possible guarantee that the objectives
of various individual allies who seek alliance are coherent.
Each individual acts entirely to their own agenda, whatever
the appearances a confused individual may generate or
imagine.

There is much confusion between
the idea of an act, and the idea of an object. Reality
is that the terms ‘act’ and ‘object’
are synonyms. That is,

actions are objects.

An action is an object moving over
a chosen time-period. For example,
Aristotle sitting on a chair for two minutes ‘is’
an object we may decide to call Aristotle. Archimedes
running down the street starkers ‘is’ the
object we may decide to call Archimedes. Any object is
changing through time. Referenting an object with a word,
such as ‘a stone’, is fundamentally not different
from referenting the running object called Archimedes.
The common distinction ‘between’ noun and
verb is therefore empirically dubious. The difference
is merely that our attention, in the case of the stone,
is not upon the movement or change of the stone. I will
leave it to you to think about where our attention may
lie in the case of Archimedes.

Individual purposes are not publicly available, only
the acts of individuals are public. Acts are not aims.
To imagine that aims may be subject to full examination
is both irrational and futile. Trust actions, not words
is the very sound advice of Machiavelli. However, words
are also actions.

Words are noises made by real mouths vibrating air and
by the writing of real marks on real substrate by real
actions. An empirical approach may be applied to test
for habitual coherence between the real words and the
real acts of individuals, and some view to consistency
may be drawn. However, keep clearly in mind the multiple
layers of potential misreading and misunderstandings to
which words are inherently subject.

(117) Priscian [(111)] [22] calls these common conceptions
“general” or “specific” because,
in one way or another, they suggest general or specific
names to us. He says universal terms are themselves, so
to speak, proper names for these conceptions. Even though
they are of confused signification as far as the named
essences are concerned, they do immediately direct the
listener’s mind to the common conception, just as
proper names do to the one thing they signify.[23]

Problems have arisen
in human communication for thousands of years because
of what are called universals. Universal words (or ‘universals’)
are words that are applied to general conceptions, words
such as ‘table’ or ‘person’. These
words do not apply to single objects that are immediately
available to the senses such as John or Jill, [24] or the approaching ’bus, or the spoon on your plate,
but are words which are applied by humans to a variety
of supposedly similar objects. There is more on this in The
Confusions of Gödel, part 1.

Humans are widely confused
into imagining that because a word may be said, a real
singular object must exist associated with that word,
but that does not follow. Universals may be imagined as
little mental programmes that differ from human to human.[24a] These programmes exist in the brains of individuals, and
they also differ subtly from individual to individual.
The differences are also unavailable for any ‘complete’
investigation. (See also Iteration (box
I).

A ‘universal’
is an ‘individual’ residing in a particular
human brain.

‘The’ and ‘a’ as prefixes tend
to qualify words as ‘individuals’ or as ‘universals’.
They are often used to lend a false air of authority.
Be cautious to ensure that a likely ‘object’
exists when a word is thus prefixed,as in a ‘bargain’, the ‘set of unicorns’ or the ‘wonderful government’.

‘truth’

Assessment of human veracity is a statistical study made
by observers. Such observances can only be applied after
the events, they are never very reliable for future events.

The perception of the correlation between words and acts
may vary wildly between actor and observer, and among
various observers. Certainties are mere illusion and self-delusion.

Mind-reading [25] is not an option.
Most humans, in their vanity, imagine far more diagnostic
power in understanding acts and motives than is rational.
If an individual is not ‘emotional’, others
tend to make wild guesses at the internal state of the
quiet individual. People may even become most peeved when
a person does not exhibit emotional noise, which state
is still often read as ‘emotion’, attributing
the quietude to all manner of paranoid interpretation
(i.e. guesses). Humans are disturbed by a lack of ‘clues’,
they often react with fear and then with aggression. Hence,
many labelled ‘normal’ exhibit a cacophony
of emotional noise, as part of their attempt to convince
or gain acceptance from others, or from sheer panic and
habitual agitation.

Individuals apply their internal understanding of various
words in accord with their individual differing experiences.
The widely held assumption that the word that you may
use has some ‘accepted’ definition is false.
Nor are your internal meanings understood with reliable
certainty by those others who may hear your words. Likewise,
your understanding of the words of others is at best approximate.

Dictionaries, at most, can give some approximation of
common usage; those definitions have no external static
certainty. Dictionaries are not authorities, they are
guide-books. It is common to imagine that ‘definitions’
in dictionaries are authoritative in everyday conversation.
This is in error for, as stated, all usages of words at
all occurrences are new. A dictionary merely attempts
to give an averaged ‘common’ usage, it can
not do more. Dictionaries provide approximate relationships
between words, not some static certainty. All such forms
of dogmatism do not meet empirical reality tests. Words,
of themselves, do not have meanings; words are dynamically
assigned meanings by local varying individual inclinations.

the world
of thought as ‘immaterial’

A major confusion arising from Aristotelian categories
is the ‘idea’ of the ‘immaterial’.
There is no (see also comments on the ontological argument and authority elsewhere) useful ‘meaning’ to ‘the
world of the immaterial’. If ‘such a world’
is ‘immaterial’, how, one may ask, is such
a world to be detected, let alone be demonstrated to another
‘individual‘? As Aristotle seemed to realise,
and as certainly did Occam, all knowledge is first in
the senses. Aristotle and others have managed down the
ages to convince themselves that ‘things’
that are ‘immaterial’, in some sense, ‘exist’,
or exist in the ‘mind’.

Now, as with Occam, in order not to multiply entities
without cause, I will take the mind to be an expression
of the brain in action. However, this is a more recent
understanding.

The ‘sort’ of ‘entity’ that was
considered ‘immaterial’ would be: ‘the’
( see to be)‘perfect’
(see ‘perfect’) circle.

Consider that the human
brain is a digital device; essentially, either neurons
fire or do not fire, rather as with transistor switches
in computers. However, the world ‘outside’
the human brain ‘is’ essentially ‘continuous’.
The human brain tends to elide differences that become
too fine for the discrimination of its peripheral systems
and its digital system. Thus, a circle is so round or
continuous that the brain cannot distinguish the small
real world variations that factually exist. In the same
way, it becomes very difficult to discriminate whether
the moon is ‘full or not a few minutes or hours
before ‘precise’ ( see ‘perfect’)
fullness.

III inside/outside
and separateness

There is no inside/outside, but it pays
to maintain such a distinction for the purposes of communication.
At the same time, you must keep clearly in mind that you
are engaged in a pragmatic strategy, you are not ‘saying’
something very meaningful about reality.

Remember that no
person ‘out there’ can see your thoughts,
they can only hear your words and watch your behaviour.
Their input is your output, while your output is their
input.

For each word you use, others will have
different meanings than your own; their meanings are drawn
out of their experiences, which experiences are always
different from your own. Similarly, each time you hear
the words of other people, be cautious that you understand
their meanings adequately for your current needs.

Look at the people outside yourself and
imagine what they can see and understand, as they look
at and listen to you. Remember, their understanding of
you is severely limited, their purposes and experience
differ from your own.

essence,
meaning and empathy

The ‘idea’ of ‘empathy’ is another
error of thought. We cannot know the mind of another,
we may only make crude guesses and do our best to understand
the messages that others signal to us. That we may at
times guess correctly the needs of another, does not turn
a guess into knowledge.

Guessing right is not being
right.

Nor can we ‘understand’ the ‘essence’
of some ‘other’ object (see box
III) that exists outside our bodies (compare with ontology section and The
error of ‘qualities’ or ‘properties’).
We may only interact with such bodies. Objects do not
have ‘meaning’; objects only have relevance
or use to us as individuals. Frogs legs have an entirely
different meaning to a French gourmet than their meaning
to the frog. We may see a stone, or interact with a stone,
but to talk of the ‘essence’ of a stone is
quite without meaning. ‘Essence’ is an introduction
of a redundant entity: taking Occam’s advice, it
is better that this primitive notion is allowed to go
into silence.

Guessing is not ‘knowledge’,
but it is the best we have.
Therefore, tolerance and patience is an essential to any
sane communication.

As individuals, we may intend meanings or signals to
others by our acts. Such gives us no strong grounds that
others will understand our intended meanings. Only by
experience and constant experiment can we build a data
bank of what will probably work for us in any given new
situation. To rail and fuss when not understood is irrational;
patience and caution are necessary to attain useful and
sane communication. (see box I).
‘Mind-reading’ is not a verifiable human attribute.

Relationships are not ‘symmetrical’ or simply
countable; ‘falling in love’ does not guarantee
reciprocity. Relationships are trades, what is value to
one may be without value to another. Of course, some are
dishonest enough to suggest the value of an object or
service is far below their real reactions. As usual, experiment
and caution are the means of progress.

You cannot read the purposes of another, only understand
as best you may. Likewise, others cannot entirely understand
you and your purposes. Tolerance of such difficulties
and differences is basic to sanity.

Tolerance and patience are not some sign of grace or
a message from the ‘immaterial’ world. Tolerance
and patience are essential to sane communication, by the
nature of reality and the human condition within that
reality.

End
notes and bibliography

abelard uses this term to
refer those who are not in contact with reality, who
are unrealistic. We can also say, "not of sound
mind."

2

gestalt:

to view as an organised whole that which is perceived
to be ‘more than’ the sum of its parts.

For example, to take the view that a ‘car is an
object which hurls us around the planet’ is to
view it as a gestalt. To view it as a bunch of tyres,
seats, carburettors and the like would be to view it
as a sum of ‘parts’.

3

empiric:

relying upon reality feedback / experiment.

4

referent:

that to which a word refers.
The word ‘stick’ refers to an object ‘out
there’ in the real world.
To say ‘the word stick’ refers to the word,
‘stick’.
Both the word ‘stick’, and the object ‘out
there’ are ‘objects’.
If this is a little confusing to you, worry not, it
will seep in over time.

Zen illustrations used to bring attention to the insufficiencies
of verbal communication, and to show the dissonance
between language and the real world (‘objects’).

6

Botvinnik, Mikhail Moiseyevich
(b. 17 Aug. [4 Aug., Old Style: the Gregorian calendar
was not introduced to Russia until the revolution!] 1911,
St. Petersburg, Russia—d. 5 May 1995, Moscow),
Soviet chess master who held the world championship three
times (1948 – 57, 1958 – 60, 1961 –
63).

7

Clanchy, M. T., Abelard,
a Medieval Life pbk, 1999, Blackwell Pub, 0631214445 £23.74 [amazon.co.uk] / $44.95 [amazon.com].
This publication lacks the rather pompous tone of much
historic writing and the author is not afraid to guess
a little. It therefore gives a good feel for the times.

Brouwer’s language is sophisticated
and personal. It takes some getting to understand. As
a starting point for those wishing to plunge into this
more deeply, see for example: Paolo Mancosu, From
Brouwer to Hilbert, pp.40 – 44
1997, OUP, pbk, ISBN-10: 0195096320 / ISBN-13: 978-0195096323Ł23.99 [amazon.co.uk] / $42.95 [amazon.com]

10

pragmatic:

what works in reality.

11

as if:

Hans Vaihinger wrote an enormous and tedious treatise
in 1911, titledThe Philosophy of ‘As If’,
in which he proposed that pragmatism is served by proceeding
on false but workable assumptions. The idea is useful,
but it did not need 370 pages! For more detail see box
III.

12

‘There’s glory for you!’
‘I don’t know what you mean by “glory”,’
Alice said.
I meant, “there’s a nice knock-down argument
for you!” ’
‘But “glory” doesn’t mean “a
nice knock-down argument”,’ Alice objected.
‘When I use a word,’ Humpty Dumpty said in
a rather scornful tone, ‘it means just what I choose
it to mean—neither more nor less.’

‘The question is,’ said Humpty Dumpty, ‘which
is to be master—that’s all.’

Skolem, T.A., ‘The foundation of
elementary arithmetic established by means of the recursive
mode of thought, without the use of apparent variables
ranging over infinite domains’,
translation in Heijenoort, J. van, From Frege To
Gödel, A Source Book of Mathematical Logic 1971,
Harvard University Press, p. 303

For
an excellent dramatisation of the right to silence see
Bolt, Robert, A Man for all Seasons, 1960
(reprinted 1990, Vintage Books, 0679728228 $9.95 [amazon.com] / amazon.co.uk

This play has been made into two films. The better (and
very good it is) is the original 1966 version, which won
6 Oscars. Play first performed in 1954$10.99 [amazon.com] / £3.99 [amazon.co.uk]

21

“Science begins when
you can measure what you are talking about and express
it in numbers.”,
W.T. Kelvin, ‘Electrical Units of Measurement’
in W.T. Kelvin, Popular
Lectures and Addresses,
vol. 1 [486pp .pdf], p.66 (1889, Macmillan)

21a

Key name for further investigations:
Occam ( also spelt as Ockham).

An example:
a suggestion that a tree spirit animates a tree.

The implications of this idea is not simple as it may
seem. Part of the success of quantum physics is to develop
a model in which there are no hidden variables, equations
are developed from actual data and encorporate only actual
data. The equations just describe the present, known situation.
The equations do not tell us what is going on, they just
describe the situation and calculate probabilities.

Using the example above: all you see is the tree growing,
that is therefore all you say. In due course, you collect
more real-world data, eventually you reach DNA.

The tree is still ‘alive’. You do not really
understand what that means, but you do not attribute it
to an extra variable like ‘god’, or the spirit
of the trees, or individual spirits in each tree, to ‘explain’
the aliveness! Nor do you even use the phrase, ‘the
quality of treeness’, as some sloppy romantics now
babble about! Thus, entities are not multiplied (or added!)
“without cause”.

Soal and Bateman, and Rhine
and Platt, published books suggesting that ‘mind-reading’
or ‘telepathy’ was part of reality. However,
the more rigour is increased; the more such supposed ‘effects’
approach zero. One of the workers on the Rhine and Pratt
study eventually admitted fraud 17 years later. Turing was taken in by this fraud. (See Turing gloss, not
yet issued, and the
logic of ethics.)
Similar dubious claims are made for mechanical ‘lie
detection’, as if measures of stress are means
of ‘mind-reading’.